Theorem cnfldsrngadd

Description: The group addition operation of a subring of the field of complex numbers. (Contributed by AV, 31-Jan-2020)

	Ref	Expression
Hypothesis	cnfldsrngbas.r	$$⊢R={ℂ}_{\mathrm{fld}}{\upharpoonright }_{𝑠}S$$
Assertion	cnfldsrngadd	$$⊢S\in V\to +={+}_R$$

Proof

Step	Hyp	Ref	Expression
1		cnfldsrngbas.r	$$⊢R={ℂ}_{\mathrm{fld}}{\upharpoonright }_{𝑠}S$$
2		cnfldadd	$$⊢+={+}_{{ℂ}_{\mathrm{fld}}}$$
3	1 2	ressplusg	$$⊢S\in V\to +={+}_R$$